Simplify. Rewrite the expression in the form $3^n$. $3^4\cdot 3^2=$
$\begin{aligned} 3^4\cdot 3^2&=3^{4+2} \\\\ &=3^{6} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 3^4\cdot 3^2&=\underbrace{3\cdot 3\cdot 3\cdot 3}_\text{4 times}\cdot\underbrace{3\cdot 3}_\text{2 times} \\\\\\ &=\underbrace{3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3}_\text{6 times} \\\\ &=3^{6} \end{aligned}$ In conclusion, $3^4\cdot 3^2=3^{6}$.